The short answer it allows you to shift to reverse with the mower deck engaged.
As the story goes, Once apon a time in Missouri two small boys were injured when the operator of a riding mower backed over them with the deck running. Following the civil court judgement JD added the RIO switch.
Before you backup, look behind you for obstructions, or pets, pull up on the RIO to the detent and then press the reverse hydro pedal. Once you are moving in reverse you can release the switch.
If you forget, no damage; just turn off the PTO and restart the engine.